KV Damping Ratio vs Hydraulic Conductivity

The Octave program, kdKVMBscan.m, permits a view of the mapped KV damping ratio as a function of hydraulic conductivity. The symbol, Kd, is used in this discussion to represent hydraulic conductivity (units $m/s$). Any good text on soil mechanics can be reviewed for the difference between absolute permeability and hydraulic conductivity. Permeability (units $m^2$) is a concept without context of fluid present. The concept of hydraulic conductivity adds the context of fluid viscosity. Thus, figures showing Kd on an axis are for a specific fluid present, and this is hard wired to water and it's viscosity.

Figure 67 shows two alternative ways to plot the representation. Hydraulic conductivity is the horizontal axis in (A), and an effective “pore diameter” in mm is shown in (B). The curves are plotted for 15 Hz shaking.

Figure 67: Octave program, kdKVMBscan.m, can be run to illustrate the effects which largely depend on porosity and frequency of shaking. Shown are the case for 15 Hz shaking. The user can choose a horizontal axis of either (A) hydraulic conductivity (m/s), or (B) “pore diameter (mm)”
\includegraphics[scale=0.8]{FigureRR}
As frequency increases, the curves would shift to the left. Frequency of shaking will be explored in the next subsection. The less permeable a soil is, the more rapidly it must be shaken to stimulate fluid motion with respect to the frame, and it is the relative motion that produces the friction. Recall that friction is measured by damping ratio. This relationship with frequency is why shear waves are dispersive in a viscous medium.